1. Field
This invention pertains to the field of measurement of surfaces of three-dimensional objects, and more particularly, to a system and method of measuring and mapping three-dimensional surfaces of spherical and aspherical objects, and of characterizing optically transmissive devices.
2. Description
There are a number of applications where the ability to provide a true measurement and map of a three-dimensional surface would be beneficial. There are also a number of applications where the ability to precisely and accurately determine characteristics (particularly one or more optical properties) of an optically transmissive device would be beneficial.
For example, contact lenses for correcting vision are produced using contact lens molds. Such contact lens molds may suffer not only from surface irregularities (small-scale features), but also may include large-area defects. Therefore, it would be desirable to provide a system and method of measuring and mapping a three-dimensional surface of a contact lens mold.
U.S. Pat. No. 6,550,917 (“the '917 patent”), from which this application claims priority, describes an improved system and method of compiling a topographic mapping of refractive errors in the eye. A disclosed system employs a wavefront sensor, such as a Shack-Hartmann wavefront sensor, and includes a combination of an adjustable telescope and a range-limiting aperture (RLA) to provide a high dynamic range measurement.
However, such a system cannot be directly applied to aspherical measurements of a contact lens mold, for example, because in most cases these elements are highly curved surfaces that cannot be probed with an injected beam system. Also, for measurements of the eye, the aberrations are known to vary according to specific classifications, such as defocus, astigmatism, coma or other higher order effects, and thus the ocular instrument could be designed a priori to deal individually with these different, known, types of aberrations.
The use of a wavefront sensor for optical metrology of optics, surfaces, optical systems, and the characterization of light beams is a well established art. Methods have been developed for: characterization of laser beams (e.g., U.S. Pat. No. 5,936,720; D. R. Neal et al., “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” S.P.I.E. 2870 (July 1996) pp.72-82); measurement of optics (e.g., D. R. Neal et al., “Wavefront sensors for control and process monitoring in optics manufacture,” S.P.I.E. 2993, pp. 211-220 (1997); J. Pfund et al., “Nonnull testing of rotationally symmetric aspheres: a systematic error assessment,” Appl. Optics 40(4) pp. 439-446 (1 Feb. 2001); and M. Abitol, “Apparatus for mapping optical elements,” U.S. Pat. No. 5,825,476); measurement of the eye and other ophthalmic systems (U.S. Pat. No. 6,550,917 (the '917 patent”)); and for many other applications. If the light incident on a wavefront sensor is the result of reflection or scattering light from a surface, then the metrology or other characteristics of the surface can be determined.
In this art several different technologies have been developed for sensing the arriving wavefront of the incident light. Among these technologies are interferometry, Shack-Hartmann wavefront sensing, Moire' deflectometry, Shearing interferometry, phase-diversity, curvature and other sensors. Each of these different types of sensors has a specific dynamic range and accuracy, along with other requirements for proper functioning of the appropriate systems. The design and selection of the appropriate phase sensitive instrument depends upon the desired characteristics of the measurement system including the desired dynamic range and accuracy.
However, in many cases the requirements for dynamic range and/or accuracy exceed the ability of a particular measurement technology. For a case where a large dynamic range is needed, the accuracy of the measurement may be reduced. If the instrument is designed to meet a specific accuracy, then it will often have reduced dynamic range. Thus one or both elements of the metrology system (dynamic range or accuracy) must be compromised in order to achieve the desired result. For example, Pfund describes a non-null test of an asphere using a Shack-Hartmann wavefront sensor approach. However, he carefully limits the application to rotationally symmetric systems so that the instrument can be operated within the dynamic range of the system. Thus his device is of limited applicability to general aspherical shapes. Abitol attempts to overcome this difficulty by marking one lenslet differently from the others. This is done by eliminating the central lenslet from the pattern of lenslets. Greater dynamic range can be achieved by extrapolating the position of this spot outwards from this marked location. However, this does not solve the problem of spot overlap or gross aberration.
There have also been a number of other methods for extending the dynamic range of the wavefront sensor purely through analysis. For example M. C. Roggeman et al., “Algorithm to increase the largest aberration that can be reconstructed from Hartmann sensor measurements,” Appl. Optics 37(20), pp. 4321-4329 (10 Jul. 1998) proposed a method for using image metrics from a separate camera to improve the dynamic range, and Pfund et al., “Dynamic range expansion of a Shack-Hartmann sensor by using a modified unwrapping algorithm,” Opt. Letters 23, pp. 995-997 (1998) proposed a method for analyzing the Shack-Hartmann image by use of a modified unwrapping algorithm. While these concepts are useful (in fact, one such method that has particular advantages is disclosed in detail below), they do not solve the problem of spot crossover when large changes in the wavefront gradient need to be measured.
The '917 patent discloses a method for the measurement of the eye that includes, among other elements, an adjustable position optical system that provides for an extension of the dynamic range of a wavefront sensor for measurement of ocular systems. This method provided a means for adjusting a reference sphere through the movement of one optical element relative to another optical element, and thus providing a means for limiting the dynamic range of the wavefront that is incident upon the sensor. A means for finding the appropriate location of this sphere was provided through feedback from the sensor.
This system has the advantage of incorporating a very large dynamic range, while still providing excellent accuracy. In this instrument, the defocus term was subtracted optically so that the residual aberrations were within the dynamic range of the wavefront sensor. However, it was applicable primarily to ocular systems that i) permitted injection of a small diameter beam, and ii) had well separated aberrations where focus dominated the strength of other aberrations. For an arbitrary aspherical optic, these features are not necessarily present.
Accordingly, it would be advantageous to provide a system and method of measuring and mapping three-dimensional surfaces of spherical and aspherical objects. It would also be advantageous to provide such a system and method that operates with an improved dynamic range. Other and further objects and advantages will appear hereinafter.
The present invention is directed to a system and method of measuring and mapping three-dimensional structures.
In one aspect of the invention, a variable position optical system and a dynamic-range-limiting aperture are used, similar to that disclosed in the '917 patent, to ensure that a wavefront sensor operates always within its dynamic range. It is recognized that for an arbitrary optical device with strongly varying surface curvatures, it will not be possible to measure the entire element in a single operation (as it is for the ocular system using the system disclosed in the '917 patent). However, the inventors have recognized that, with different positions of the variable position optical system, it is possible to examine the entire surface of the element under test. Thus by systematically varying the position of the variable position optical system, it is possible to obtain measurements of the entire surface of the element under test, and then construct the measurement of a highly curved or aberrated element from these multiple individual measurements.
In another aspect of the invention, a system for controlling, directing, and modulating light is used to project light onto an element under test, collect the light reflected from this element, direct light through a dynamic-range-limiting aperture, and project this light onto a wavefront sensor. This system may include optical reformatting optics to appropriately reform the light from collimated to converging or diverging as needed for the element under test.
In another aspect of this invention, a series of wavefront measurements are “stitched” together using mathematical methods. Each of these measurements would be acquired using a different optical system aspect (such as focus, tilt or other systematically introduced reference aberration), in conjunction with a means for limiting the dynamic range of the wavefront incident on a wavefront sensor (beneficially, through a dynamic-range-limiting aperture), so that a series of accurate, independent measurements are acquired from the element under test. Using the a priori reference information, each individual measurement wavefront is corrected appropriately. These measurements may then be combined together to produce an overall measurement of the entire surface of the element under test using the mathematical methods disclosed herein.
Accordingly, in one aspect of the invention, a system for mapping a surface of a three-dimensional object, comprises: a projecting optical system adapted to project light onto an object; a pre-correction system adapted to compensate a light beam to be projected onto the object for aberrations in the object, the pre-correction system being positioned in between the projecting optical system and the object; an imaging system adapted to collect light scattered by the object; and a wavefront sensor adapted to receive the light collected by the imaging system.
In another aspect of the invention, a method of mapping a surface of an object, comprises: projecting a light beam onto an object; compensating the light beam to be projected onto the object for aberrations in the object; collecting light scattered by the object; and sensing a wavefront of the collected light scattered by the object.
In yet another aspect of the invention, a system for measuring an optical characteristic of an optically transmissive object, comprises: a projecting optical system which projects light through an optically transmissive object; a correction system adapted to at least partially compensate a light beam that has been projected through the object for at least one optical property of the object; an imaging system adapted to collect the light that has been projected through the object; and a wavefront sensor adapted to receive the light collected by the imaging system.
In another aspect of the invention, a method of measuring an optical quality of an optically transmissive object, comprises: projecting a light beam through an optically transmissive object; at least partially compensating the light beam that has been projected through the object for at least one optical property of the object; collecting the light beam that has been projected through the object; and sensing a wavefront of the collected light.
In another aspect of the invention, a method of mapping a surface of an object, comprises: (a) projecting a light beam onto a surface of an object; (b) collecting light scattered by a first portion of the surface of the object and rejecting light scattered by a second portion of the surface of the object; (c) sensing a wavefront of the collected light returned by the portion of the surface of the object; (d) repeating steps (a) through (c) for a plurality of different portions of the surface of the object that together span a target area of the surface of the object; and (e) stitching together the sensed wavefronts to produce a complete measurement of the target area of the surface of the object.
In another aspect of the invention, a method of measuring an optically transmissive object, comprises: (a) projecting a light beam through a portion of an object; (b) collecting light passed through the portion of the object; (c) sensing a wavefront of the collected light passed through the portion of the object; (d) repeating steps (a) through (c) for a plurality of different portions of the object that together span a target area of the object; and (e) stitching together the sensed wavefronts to produce a complete measurement of the target area of the object.
In another aspect of the invention, a method of mapping a surface of an object, comprises: (a) locating a light source a first distance from an object; (b) projecting a light beam from the light source onto a surface of the object; (c) collecting light scattered by the surface of the object; (d) sensing a wavefront comprising a difference between a wavefront of the collected light and a reference wavefront; (e) changing the distance between the light source and the object; (f) repeating steps (b) through (e) to produce N sensed wavefronts; and (g) stitching together the N sensed wavefronts to produce a complete measurement of the target area of the surface of the object.
In another aspect of the invention, a method of measuring an optically transmissive object, comprises: (a) locating a light source a first distance from an optically transmissive object; (b) projecting a light beam from the light source through the object; (c) collecting light projected through the object; (d) sensing a wavefront comprising a difference between a wavefront of the collected light and a reference wavefront; (e) changing the distance between the light source and the object; (f) repeating steps (b) through (e) N times to produce N sensed wavefronts; and (g) stitching together the N sensed wavefronts to produce a complete measurement of the target area of the surface of the object.
In another aspect of the invention, a point light source for producing a spherical wave, comprises: a light source; a diffuser adapted to receive light from the light source; and a structure having an aperture adapted to receive and pass therethrough the light from the diffuser.
In another aspect of the invention, a method of determining when a portion of a light wavefront received by a wavefront sensor exceeds the dynamic range of the wavefront sensor, comprises: assigning a group of N pixels of a wavefront sensor to a focal spot; providing a first light wavefront to the wavefront sensor under conditions known to be within a dynamic range of the wavefront sensor; calculating a reference value, ΦkREF, for a second moment of the focal spot produced by the first light wavefront within the group of N pixels; providing a second light wavefront to the wavefront sensor; calculating a value of the Φk, for a second moment of the focal spot produced by the second light wavefront within the group of N pixels; and determining that the second light wavefront is within the dynamic range of the wavefront sensor within the group of N pixels when: |σk−σkREF|<tσ, where tΦ is a set threshold value.
In another aspect of the invention, a method of mapping a surface of an object, comprises: projecting a light beam onto an object; compensating the light beam to be projected onto the object for aberrations in the object; passing light scattered by the object through a dynamic-range-limiting aperture; collecting light passed through the dynamic-range-limiting aperture; and sensing a wavefront of the collected light.
In another aspect of the invention, a method of determining a position of a focal spot on a wavefront sensor, comprises: assigning a first group of N pixels of a wavefront sensor to a focal spot; providing a light wavefront to the wavefront sensor; measuring an irradiance distribution of the light wavefront across the N pixels of the first group; calculating a preliminary centroid position of the focal spot as a first moment of the irradiance distribution of the light wavefront across the N pixels of the first group; assigning a second group of N pixels of the wavefront sensor to the focal spot, where the second group of N pixels is approximately centered at the preliminary centroid position; and calculating a location of the focal spot as a first moment of the power of irradiance distribution of the light wavefront across the N pixels of the second group.
In another aspect of the invention, a method of determining a wavefront of light received by a wavefront sensor, comprises: (a) providing a light wavefront to a wavefront sensor; (b) assigning pixels of the wavefront sensor to a first plurality of areas-of-interest (AOIs); (c) determining a first region of the wavefront sensor where the received light wavefront is within a dynamic range of the wavefront sensor for all AOIs within the first region; (d) calculating locations for centers of light spots of received light for all AOIs within the first region; (e) calculated a fitted wavefront for the received light wavefront over the first region; (f) computing a slope of the fitted wavefront at each AOI within the first region; (g) projecting locations for centers of light spots of received light for a second region of the wavefront sensor larger than the first region, using the slopes of the fitted wavefront within the first region; (h) reassigning the pixels of the wavefront sensor to a second plurality of areas-of-interest (AOIs) each centered on one of the calculated or projected centers of light spots; (i) determining a new first region of the wavefront sensor where the received light wavefront is within a dynamic range of the wavefront sensor for all AOIs; and (j) repeating steps (d) through (i) until one of: (i) the new first region is no larger than a previous first region; and (ii) the new first region spans substantially the entire wavefront sensor.
In another aspect of the invention, a method of measuring a focal length (F) of a lens, comprises: (a) locating a light source on a first side of a lens, one of the light source and the lens being located at a position Zi; (b) locating a wavefront sensor a fixed distance (L) from the lens on a second side thereof; (c) projecting a light beam from the light source through the lens; (d) collecting light passed through lens; (e) sensing a wavefront of the collected light at the wavefront sensor; (f) measuring a corresponding vergence Pi of the light; (g) incrementing i by 1, and moving the position of one of the light source and the lens to a new position Zi; (h) repeating steps (c) through (g) to obtain N values of Zi and Pi; and
(i) applying the N values of Zi and Pi to a least squares fit algorithm to solve for the focal length (F).